It is known to etch micromechanical surface structures in a silicon layer in hydrofluoride acid vapor and, to achieve an undercut of a structured surface layer of silicon, to apply a sacrificial layer of silicon dioxide under the surface layer to be structured. In this context, the hydrofluoride acid vapor, in etching the sacrificial layer, effects a purely time-controlled undercut of the structured surface layer, so that the specific undercut width achieved in the sacrificial layer, for example, to bring about the defined exposure of free-standing sensor structures in the surface layer, is not directly measurable in the course of the hydrofluoride acid vapor undercut, or cannot be monitored during the etching. Therefore, the permanent danger exists of inadvertently etching too briefly or too long. In particular, an etching lasting too long can lead to the destruction of structures on a wafer, for example, by detaching them from the substrate.